On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

We prove the existence of solutions to the nonlinear Schrödinger equation ${\epsilon }^2{(i\mathrm{?}+\mathit{A})}^{2}u+V(y)u?|u{|}^{p?1}u=0$ in ${\mathbb{R}}^2$ with a magnetic potential $\mathit{A}=(A_1,A_2)$. Here V represents the electric potential, the index p is greater than 1. Along some sequence $\{{\epsilon }_n\}$ tending to zero we exhibit complex-value solutions that concentrate along some closed curves.     

Nanosized cation exchanger for the electrophoretic separation and preconcentration of catecholamines and amino acids

The first example of application of nanosized polystyrene-based cation exchanger (NSCE) with sulfo groups as a dynamic coating of capillary walls was demonstrated. The conditions of dynamic coating formation were optimized and ensured the long-term stability of the coating. Capillary-to-capillary and day-to-day repeatabilities were 4% and 3%, correspondingly. The NSCE coating stability at various pH and influence of pH on the EOF mobility were investigated. The developed NSCE-modified coated capillaries provided improved resolution (R_s = 0.9–3.2 for catecholamines and R_s = 1.7–2.8 for amino acids) and efficiencies (330–520 ×10³ t.p./m) of basic analytes, which are 1.5 times higher compared to untreated capillary. The optimized conditions were as follows: 50 mM phosphate buffer solution at pH 2.2 with 5 μM NSCE. The effect of the NSCE concentration in BGE on the electrophoretic mobilities of the analytes was investigated. The various online concentration techniques were tested in order to decrease the LODs. The simultaneous application of NSCE capillaries and field-amplified sample stacking provided the lowest LODs of catecholamines and amino acids and allowed to determine these analytes in human urine.     

融合图卷积神经网络和注意力机制的PM2.5小时浓度多步预测

PM_2.5小时浓度多为单步预测。为实现PM_2.5小时浓度的多步预测，基于“编码器-解码器”的序列-序列预测（Seq2Seq）模型，集合图卷积神经网络提取非欧式空间数据特征的能力以及注意力机制自适应关注特征的能力，提出了融合图卷积神经网络和注意力机制的PM_2.5小时浓度多步预测（GCN_Attention_Seq2Seq）模型。并与Seq2Seq模型和使用了图卷积神经网络、未使用注意力机制的GCN_Seq2Seq模型进行了对照，以2015—2016年北京市22个空气质量监测站点的空气质量数据为样本进行实例验证，结果表明，Seq2Seq模型和图卷积神经网络（GCN）可对PM_2.5小时浓度数据的时空依赖进行有效建模，注意力机制有助于减缓多步预测中的预测精度衰减，提升PM_2.5小时浓度多步预测的精度。GCN_Attention_Seq2Seq模型可有效应用于多种长度的PM_2.5浓度预测窗口。     

Capillary zone electrophoresis of lipoarabinomannan by multi-layered concentration

The present article describes a capillary zone electrophoresis method which relies on a multilayered water-alkali solvent stacking with online ionization to enhance detection of mannose, arabinose, and their oligosaccharides, which are used as the migration profile standards but are also the distinctive structural components of lipoarabinomannan. Lipoarabinomannan is detected in patients having tuberculosis. The capillary electrophoresis method with ionization of the whole saccharides without degradation in alkaline solution inside the capillary is based on the structural deprotonation of the molecules under ultrahigh pH conditions. The validation of the capillary electrophoresis parameters revealed that the 15-fold electrolyte–water-injection plug allowed detection of one-third lower concentrations than detected without online concentration. For the first time, the better detectability was seen especially for highly polymerized, but otherwise poorly ionized, arabinooctaose. The applicability of the method for detecting whole large biological saccharide complexes was confirmed by the glycolipid lipoarabinomannan. For the first time also, the migration of the indestructible lipoarabinomannan was detected together with oligosaccharides used representing the capping units, namely mannose, mannobiose, and mannotriose. The myo-inositol-phosphate-lipid unit was seen to migrate separately from the arabinomannan, since it was hydrolyzed from one lipoarabinomannan product under alkaline conditions in capillary electrophoresis.     

Circular Dichroism of Amino Acids: Following the Structural Formation of Phenylalanine

Circular dichroism (CD) is frequently used to assess the secondary structure of peptides and proteins, whereas less attention has been given to their building blocks, that is, single amino acids, as they do not possess a secondary structure. Here, we follow the CD signal of amino acids and reveal that several acids exhibit a unique CD pattern as a function of their concentration. Accordingly, we propose an eight‐level classification of the CD signal of the various amino acids. Special focus is given to the CD pattern of phenylalanine (Phe), for which we observe the formation of an ultra‐narrow CD peak (full width at high maximum of only 5 nm). This CD peak can be attributed to the formation of Phe‐based chiral structural features. Further support for the formation of an ordered structure is given by using NMR, and the additional self‐assembly process of Phe to tubular structures.     

Facile Formation of Sulfurized Nanorod-Like ZnO/Zn(OH)2 and Hierarchical Flower-Like γ-Zn(OH)2/ϵ-Zn(OH)2 from a Green Synthesis and Application as Luminescent Solar Concentrator

This research endeavors to overcome the significant challenge of developing materials that simultaneously possess photostability and photosensitivity to UV-visible irradiation. Sulfurized nanorod (NR)-like ZnO/Zn(OH)₂ and hierarchical flower-like γ-Zn(OH)₂/ϵ-Zn(OH)₂ were identified from XRD diffraction patterns and Raman vibrational modes. The sulfurized material, observed by FEG-SEM and TEM, showed diameters ranging from 10 and 40 nm and lengths exceeding 200 nm. The S²⁻ ions intercalated Zn²⁺, modulating NRs to dumbbell-like microrods. SAED and HRTEM illustrated the atomic structure in (101) crystal plane. Its direct band gap of 3.0 eV was attributed to the oxygen vacancies, which also contribute to the deep-level emissions at 422 and 485 nm. BET indicated specific surface area of 4.4 m² g⁻¹ and pore size as mesoporosity, which are higher compared to the non-sulfurized analogue. These findings were consistent with the observed photocurrent, photostability and photoluminescence (PL), further supporting the suitability of sulfurized NR-like ZnO/Zn(OH)₂ as a promising candidate for Luminescent solar concentrators (LSC)-photovoltaic (PV) system.     

The Prenucleation Equilibrium of the Parathyroid Hormone Determines the Critical Aggregation Concentration and Amyloid Fibril Nucleation

Nucleation and growth of amyloid fibrils were found to only occur in supersaturated solutions above a critical concentration (c_crit). The biophysical meaning of c_crit remained mostly obscure, since typical low values of c_crit in the sub-μM range hamper investigations of potential oligomeric states and their structure. Here, we investigate the parathyroid hormone PTH₈₄ as an example of a functional amyloid fibril forming peptide with a comparably high c_crit of 67±21 μM. We describe a complex concentration dependent prenucleation ensemble of oligomers of different sizes and secondary structure compositions and highlight the occurrence of a trimer and tetramer at c_crit as possible precursors for primary fibril nucleation. Furthermore, the soluble state found in equilibrium with fibrils adopts to the prenucleation state present at c_crit. Our study sheds light onto early events of amyloid formation directly related to the critical concentration and underlines oligomer formation as a key feature of fibril nucleation. Our results contribute to a deeper understanding of the determinants of supersaturated peptide solutions. In the current study we present a biophysical approach to investigate c_crit of amyloid fibril formation of PTH₈₄ in terms of secondary structure, cluster size and residue resolved intermolecular interactions during oligomer formation. Throughout the investigated range of concentrations (1 μM to 500 μM) we found different states of oligomerization with varying ability to contribute to primary fibril nucleation and with a concentration dependent equilibrium. In this context, we identified the previously described c_crit of PTH₈₄ to mark a minimum concentration for the formation of homo-trimers/tetramers. These investigations allowed us to characterize molecular interactions of various oligomeric states that are further converted into elongation competent fibril nuclei during the lag phase of a functional amyloid forming peptide.     

Coupling Effects of Electrostatic Interactions and Salt Concentration Gradient in Polymer Translocation through a Nanopore: A Coarse-Grained Molecular Dynamics Simulations Study

We study the influence of polymer pore interactions and focus on the role played by the concentration gradient of salt in the translocation of polyelectrolytes (PE) through nanopores explicitly using coarse-grained Langevin dynamics simulations. The mean translocation time is calculated by varying the applied voltage, the pH, and the salt concentration gradient. Changing the pH can alter the electrostatic interaction between the protein pore and the polyelectrolyte chain. The polymer pore interaction is weakened by the increase in the strength of the externally applied electric field that drives translocation. Additionally, the screening effect of the salt can reduce the strong charge-charge repulsion between the PE beads which can make translocation faster. The simulation results show there can be antagonistic or synergistic coupling between the salt concentration-induced screening effect and the drift force originating from the salt concentration gradient thereby affecting the translocation time. Our simulation results are explained qualitatively with free energy calculations.